//

#ifndef ABEL_RANDOM_ZIPF_DISTRIBUTION_H_
#define ABEL_RANDOM_ZIPF_DISTRIBUTION_H_

#include <cassert>
#include <cmath>
#include <istream>
#include <limits>
#include <ostream>
#include <type_traits>

#include "abel/random/internal/iostream_state_saver.h"
#include "abel/random/uniform_real_distribution.h"

namespace abel {


// abel::zipf_distribution produces random integer-values in the range [0, k],
// distributed according to the discrete probability function:
//
//  P(x) = (v + x) ^ -q
//
// The parameter `v` must be greater than 0 and the parameter `q` must be
// greater than 1. If either of these parameters take invalid values then the
// behavior is undefined.
//
// IntType is the result_type generated by the generator. It must be of integral
// type; a static_assert ensures this is the case.
//
// The implementation is based on W.Hormann, G.Derflinger:
//
// "Rejection-Inversion to Generate Variates from Monotone Discrete
// Distributions"
//
// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
//
template<typename IntType = int>
class zipf_distribution {
  public:
    using result_type = IntType;

    class param_type {
      public:
        using distribution_type = zipf_distribution;

        // Preconditions: k > 0, v > 0, q > 1
        // The precondidtions are validated when NDEBUG is not defined via
        // a pair of assert() directives.
        // If NDEBUG is defined and either or both of these parameters take invalid
        // values, the behavior of the class is undefined.
        explicit param_type(result_type k = (std::numeric_limits<IntType>::max)(),
                            double q = 2.0, double v = 1.0);

        result_type k() const { return k_; }

        double q() const { return q_; }

        double v() const { return v_; }

        friend bool operator==(const param_type &a, const param_type &b) {
            return a.k_ == b.k_ && a.q_ == b.q_ && a.v_ == b.v_;
        }

        friend bool operator!=(const param_type &a, const param_type &b) {
            return !(a == b);
        }

      private:
        friend class zipf_distribution;

        ABEL_FORCE_INLINE double h(double x) const;

        ABEL_FORCE_INLINE double hinv(double x) const;

        ABEL_FORCE_INLINE double compute_s() const;

        ABEL_FORCE_INLINE double pow_negative_q(double x) const;

        // Parameters here are exactly the same as the parameters of Algorithm ZRI
        // in the paper.
        IntType k_;
        double q_;
        double v_;

        double one_minus_q_;  // 1-q
        double s_;
        double one_minus_q_inv_;  // 1 / 1-q
        double hxm_;              // h(k + 0.5)
        double hx0_minus_hxm_;    // h(x0) - h(k + 0.5)

        static_assert(std::is_integral<IntType>::value,
                      "Class-template abel::zipf_distribution<> must be "
                      "parameterized using an integral type.");
    };

    zipf_distribution()
            : zipf_distribution((std::numeric_limits<IntType>::max)()) {}

    explicit zipf_distribution(result_type k, double q = 2.0, double v = 1.0)
            : param_(k, q, v) {}

    explicit zipf_distribution(const param_type &p) : param_(p) {}

    void reset() {}

    template<typename URBG>
    result_type operator()(URBG &g) {  // NOLINT(runtime/references)
        return (*this)(g, param_);
    }

    template<typename URBG>
    result_type operator()(URBG &g,  // NOLINT(runtime/references)
                           const param_type &p);

    result_type k() const { return param_.k(); }

    double q() const { return param_.q(); }

    double v() const { return param_.v(); }

    param_type param() const { return param_; }

    void param(const param_type &p) { param_ = p; }

    result_type (min)() const { return 0; }

    result_type (max)() const { return k(); }

    friend bool operator==(const zipf_distribution &a,
                           const zipf_distribution &b) {
        return a.param_ == b.param_;
    }

    friend bool operator!=(const zipf_distribution &a,
                           const zipf_distribution &b) {
        return a.param_ != b.param_;
    }

  private:
    param_type param_;
};

// --------------------------------------------------------------------------
// Implementation details follow
// --------------------------------------------------------------------------

template<typename IntType>
zipf_distribution<IntType>::param_type::param_type(
        typename zipf_distribution<IntType>::result_type k, double q, double v)
        : k_(k), q_(q), v_(v), one_minus_q_(1 - q) {
    assert(q > 1);
    assert(v > 0);
    assert(k > 0);
    one_minus_q_inv_ = 1 / one_minus_q_;

    // Setup for the ZRI algorithm (pg 17 of the paper).
    // Compute: h(i max) => h(k + 0.5)
    constexpr double kMax = 18446744073709549568.0;
    double kd = static_cast<double>(k);
    // TODO(abel-team): Determine if this check is needed, and if so, add a test
    // that fails for k > kMax
    if (kd > kMax) {
        // Ensure that our maximum value is capped to a value which will
        // round-trip back through double.
        kd = kMax;
    }
    hxm_ = h(kd + 0.5);

    // Compute: h(0)
    const bool use_precomputed = (v == 1.0 && q == 2.0);
    const double h0x5 = use_precomputed ? (-1.0 / 1.5)  // exp(-log(1.5))
                                        : h(0.5);
    const double elogv_q = (v_ == 1.0) ? 1 : pow_negative_q(v_);

    // h(0) = h(0.5) - exp(log(v) * -q)
    hx0_minus_hxm_ = (h0x5 - elogv_q) - hxm_;

    // And s
    s_ = use_precomputed ? 0.46153846153846123 : compute_s();
}

template<typename IntType>
double zipf_distribution<IntType>::param_type::h(double x) const {
    // std::exp(one_minus_q_ * std::log(v_ + x)) * one_minus_q_inv_;
    x += v_;
    return (one_minus_q_ == -1.0)
           ? (-1.0 / x)  // -exp(-log(x))
           : (std::exp(std::log(x) * one_minus_q_) * one_minus_q_inv_);
}

template<typename IntType>
double zipf_distribution<IntType>::param_type::hinv(double x) const {
    // std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)) - v_;
    return -v_ + ((one_minus_q_ == -1.0)
                  ? (-1.0 / x)  // exp(-log(-x))
                  : std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)));
}

template<typename IntType>
double zipf_distribution<IntType>::param_type::compute_s() const {
    // 1 - hinv(h(1.5) - std::exp(std::log(v_ + 1) * -q_));
    return 1.0 - hinv(h(1.5) - pow_negative_q(v_ + 1.0));
}

template<typename IntType>
double zipf_distribution<IntType>::param_type::pow_negative_q(double x) const {
    // std::exp(std::log(x) * -q_);
    return q_ == 2.0 ? (1.0 / (x * x)) : std::exp(std::log(x) * -q_);
}

template<typename IntType>
template<typename URBG>
typename zipf_distribution<IntType>::result_type
zipf_distribution<IntType>::operator()(
        URBG &g, const param_type &p) {  // NOLINT(runtime/references)
    abel::uniform_real_distribution<double> uniform_double;
    double k;
    for (;;) {
        const double v = uniform_double(g);
        const double u = p.hxm_ + v * p.hx0_minus_hxm_;
        const double x = p.hinv(u);
        k = rint(x);              // std::floor(x + 0.5);
        if (k > p.k()) continue;  // reject k > max_k
        if (k - x <= p.s_) break;
        const double h = p.h(k + 0.5);
        const double r = p.pow_negative_q(p.v_ + k);
        if (u >= h - r) break;
    }
    IntType ki = static_cast<IntType>(k);
    assert(ki <= p.k_);
    return ki;
}

template<typename CharT, typename Traits, typename IntType>
std::basic_ostream<CharT, Traits> &operator<<(
        std::basic_ostream<CharT, Traits> &os,  // NOLINT(runtime/references)
        const zipf_distribution<IntType> &x) {
    using stream_type =
    typename random_internal::stream_format_type<IntType>::type;
    auto saver = random_internal::make_ostream_state_saver(os);
    os.precision(random_internal::stream_precision_helper<double>::kPrecision);
    os << static_cast<stream_type>(x.k()) << os.fill() << x.q() << os.fill()
       << x.v();
    return os;
}

template<typename CharT, typename Traits, typename IntType>
std::basic_istream<CharT, Traits> &operator>>(
        std::basic_istream<CharT, Traits> &is,  // NOLINT(runtime/references)
        zipf_distribution<IntType> &x) {        // NOLINT(runtime/references)
    using result_type = typename zipf_distribution<IntType>::result_type;
    using param_type = typename zipf_distribution<IntType>::param_type;
    using stream_type =
    typename random_internal::stream_format_type<IntType>::type;
    stream_type k;
    double q;
    double v;

    auto saver = random_internal::make_istream_state_saver(is);
    is >> k >> q >> v;
    if (!is.fail()) {
        x.param(param_type(static_cast<result_type>(k), q, v));
    }
    return is;
}


}  // namespace abel

#endif  // ABEL_RANDOM_ZIPF_DISTRIBUTION_H_
